A model is a precise, mathematical representation of the dynamics of a system used to provide insight into the behavior of that system. As a matter of definition, the term “system” refers to a set or collection of equations that can be dealt with collectively. A linear system refers to a finite set of linear equations, defined herein to include those equations that graph as straight lines in the Cartesian coordinate system. Therefore, in mathematics, a linear system is a collection of two or more linear equations involving the same set of variables. As a mathematical abstraction, linear systems have been applied advantageously in automatic control theory, signal processing, and telecommunications. For example, the propagation media for wireless communication systems may be modeled as linear systems.
Modeling solutions known in the art typically employ computational methods that seek to exercise a set of linear systems in order to test, verify, and/or observe inputs and outputs of that set of linear systems. In such methods, the linear system(s) may model naturally occurring phenomena or environments, and the inputs and outputs are often real, virtual, and/or simulated. Modeling of this type may provide a certain level of repeatability that may not be possible to obtain in real world testing, and also may maintain a reasonable level of realism that may approximate that of real world testing. These modeling solutions are referred to herein as emulators and/or simulators.
As used herein, simulation may be construed to involve replicating the general behavior of a system starting from a conceptual model. Also as used herein, emulation may be construed to involve replicating in a second system how a first system internally works considering each function and their relations. Existing wireless emulators, and some simulators, model the behavior of a given wireless network environment for purposes of testing or analyzing a wireless network design that may feature multiple radio frequency (RF) devices, be they real, simulated, or virtual.
For example, and without limitation, the block diagrams shown at FIGS. 1, 2 and 3 illustrate a generic modeling method known in the prior art. As described above, the inputs and outputs of such models may be real, virtual, and/or simulated. More specifically, the block diagram 300 shown at FIG. 2 illustrates an exemplary linear system (LS) 302. Linear systems modeled by emulators/simulators may be generally divided into two parts, as shown: an impulse response model (IRM) 310 and a model for an overall delay and gain/loss (DGLM) value 320. Such linear system models may employ the linear system operations shown in FIG. 1 (i.e., fading operations 210 each with its inputs 212 and outputs 214, a path loss operation 220 with its inputs 222 and outputs 224, a delay operation 230 with its inputs 232 and outputs 234, and combine operations 240 each with its inputs 242, 244 and output 246).
Referring now to the prior art model illustrated at FIG. 3, and continuing to refer to FIG. 2, each Kth input 330 in a set of inputs and each Lth output 340 in a set of outputs may have a unique and independent value for each impulse of its respective linear system 302 in the set of linear systems (specifically, for its respective IRM 310 from FIG. 2). As such, a certain amount of processing resources and time is required to model the respective IRM 310 and DGLM 320 for each of the linear systems 302 present in the model 400. The set of linear systems in such a model 400 is often calculated using some type of processing unit, such as, but not limited to, central processing units (CPUs), graphics processing units (GPUs), digital signal processors (DSPs), and field-programmable gate arrays (FPGAs).
FIG. 3A illustrates an exploded view of the model 400 of FIG. 3 that, for example, and without limitation, may model a wireless emulator characterized by only path loss 220 and propagation delay 230 (as defined above and as illustrated in FIG. 1) in a network of interest that services K transmitters (inputs) 330 and L receivers (outputs) 340. Each transmitter-receiver combination creates a path between them. Therefore, the model comprises LK paths, and each path is associated with a respective delay component Δ 230 and a respective path loss component Γ 220. Consequently, solving the set of linear systems representing such paths requires a processing resource(s) to perform LK delay operations to compute propagation delay 230 and LK multiplications to compute path loss 220. Furthermore, the processing resources must perform L (K−1) adds to combine 240 each transmitted signal at each of the respective features. A person of ordinary skill in the art will immediately recognize that as the number of transmitters and receivers increases the number of required operations increase, and, therefore a large number of transmitter-receiver combinations (e.g., RF devices) can present computational issues when modeling such a system.
Referring now to the prior art model illustrated at FIG. 3B, and continuing to refer to FIG. 3A, introducing a fading component 210 to the path loss 220 and propagation delay 230 in the model 400 described above may add another degree of computational complexity. (Note: Fading component 210, represented as δ in FIGS. 1 and 2, is characterized by k inputs, l outputs, and m multipath channels, the latter described in detail below. For illustration purposes, fading component 210, represented as h in FIG. 3B, is characterized by k inputs and l outputs only, and without accounting for multipath.) As with the path loss component Γ 220, network architects typically multiply each path by a fading component h 210 as shown in FIG. 3B. Doing so may add another LK multiplication functions to the linear system model 400 to implement fading.
Introducing multipath effects complicates the model further. In wireless telecommunications, multipath is a propagation phenomenon resulting from radio signals reaching a receiver by two or more paths. Causes of multipath may include atmospheric ducting, ionospheric reflection and refraction, and reflection from water bodies and terrestrial objects such as mountains and buildings. Introducing multipath to the linear system model 400 results in a number of multipliers equal to MLK, where M is the number of multipath components. Such a model modification also results in MLK delay operations, and (M−1) LK add operations.
A need exists for specific improvements in how a computer operates to model a set of linear systems. More specifically, a need exists for improvements in the state of the art for simulating/emulating wireless network architectures.
This background information is provided to reveal information believed by the applicant to be of possible relevance to the present invention. No admission is necessarily intended, nor should be construed, that any of the preceding information constitutes prior art against the present invention.